bandpass butterworth filter implementation in C++
Solution 1
I finally found it. I just need to implement the following code from matlab source code to c++ . "the_mandrill" were right, I need to add the normalizing constant into the coefficient:
kern = exp(-j*w*(0:length(b)-1));
b = real(b*(kern*den(:))/(kern*b(:)));
EDIT: and here is the final edition, which the whole code will return numbers exactly equal to MATLAB :
double *ComputeNumCoeffs(int FilterOrder,double Lcutoff, double Ucutoff, double *DenC)
{
double *TCoeffs;
double *NumCoeffs;
std::complex<double> *NormalizedKernel;
double Numbers[11]={0,1,2,3,4,5,6,7,8,9,10};
int i;
NumCoeffs = (double *)calloc( 2*FilterOrder+1, sizeof(double) );
if( NumCoeffs == NULL ) return( NULL );
NormalizedKernel = (std::complex<double> *)calloc( 2*FilterOrder+1, sizeof(std::complex<double>) );
if( NormalizedKernel == NULL ) return( NULL );
TCoeffs = ComputeHP(FilterOrder);
if( TCoeffs == NULL ) return( NULL );
for( i = 0; i < FilterOrder; ++i)
{
NumCoeffs[2*i] = TCoeffs[i];
NumCoeffs[2*i+1] = 0.0;
}
NumCoeffs[2*FilterOrder] = TCoeffs[FilterOrder];
double cp[2];
double Bw, Wn;
cp[0] = 2*2.0*tan(PI * Lcutoff/ 2.0);
cp[1] = 2*2.0*tan(PI * Ucutoff / 2.0);
Bw = cp[1] - cp[0];
//center frequency
Wn = sqrt(cp[0]*cp[1]);
Wn = 2*atan2(Wn,4);
double kern;
const std::complex<double> result = std::complex<double>(-1,0);
for(int k = 0; k<11; k++)
{
NormalizedKernel[k] = std::exp(-sqrt(result)*Wn*Numbers[k]);
}
double b=0;
double den=0;
for(int d = 0; d<11; d++)
{
b+=real(NormalizedKernel[d]*NumCoeffs[d]);
den+=real(NormalizedKernel[d]*DenC[d]);
}
for(int c = 0; c<11; c++)
{
NumCoeffs[c]=(NumCoeffs[c]*den)/b;
}
free(TCoeffs);
return NumCoeffs;
}
Solution 2
I know this is a post on an old thread, and I would usually leave this as a comment, but I'm apparently not able to do that.
In any case, for people searching for similar code, I thought I would post the link from where this code originates (it also has C code for other types of Butterworth filter coefficients and some other cool signal processing code).
The code is located here: http://www.exstrom.com/journal/sigproc/
Additionally, I think there is a piece of code which calculates said scaling factor for you already.
/**********************************************************************
sf_bwbp - calculates the scaling factor for a butterworth bandpass filter.
The scaling factor is what the c coefficients must be multiplied by so
that the filter response has a maximum value of 1.
*/
double sf_bwbp( int n, double f1f, double f2f )
{
int k; // loop variables
double ctt; // cotangent of theta
double sfr, sfi; // real and imaginary parts of the scaling factor
double parg; // pole angle
double sparg; // sine of pole angle
double cparg; // cosine of pole angle
double a, b, c; // workspace variables
ctt = 1.0 / tan(M_PI * (f2f - f1f) / 2.0);
sfr = 1.0;
sfi = 0.0;
for( k = 0; k < n; ++k )
{
parg = M_PI * (double)(2*k+1)/(double)(2*n);
sparg = ctt + sin(parg);
cparg = cos(parg);
a = (sfr + sfi)*(sparg - cparg);
b = sfr * sparg;
c = -sfi * cparg;
sfr = b - c;
sfi = a - b - c;
}
return( 1.0 / sfr );
}
user261002
Updated on July 26, 2022Comments
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user261002 almost 2 years
I am implementing an image analysis algorithm using openCV and c++, but I found out openCV doesnt have any function for Butterworth Bandpass filter officially. in my project I have to pass a time series of pixels into the Butterworth 5 order filter and the function will return the filtered time series pixels. Butterworth(pixelseries,order, frequency), if you have any idea to help me of how to start please let me know. Thank you
EDIT : after getting help, finally I come up with the following code. which can calculate the Numerator Coefficients and Denominator Coefficients, but the problem is that some of the numbers is not as same as matlab results. here is my code:
#include <iostream> #include <stdio.h> #include <vector> #include <math.h> using namespace std; #define N 10 //The number of images which construct a time series for each pixel #define PI 3.14159 double *ComputeLP( int FilterOrder ) { double *NumCoeffs; int m; int i; NumCoeffs = (double *)calloc( FilterOrder+1, sizeof(double) ); if( NumCoeffs == NULL ) return( NULL ); NumCoeffs[0] = 1; NumCoeffs[1] = FilterOrder; m = FilterOrder/2; for( i=2; i <= m; ++i) { NumCoeffs[i] =(double) (FilterOrder-i+1)*NumCoeffs[i-1]/i; NumCoeffs[FilterOrder-i]= NumCoeffs[i]; } NumCoeffs[FilterOrder-1] = FilterOrder; NumCoeffs[FilterOrder] = 1; return NumCoeffs; } double *ComputeHP( int FilterOrder ) { double *NumCoeffs; int i; NumCoeffs = ComputeLP(FilterOrder); if(NumCoeffs == NULL ) return( NULL ); for( i = 0; i <= FilterOrder; ++i) if( i % 2 ) NumCoeffs[i] = -NumCoeffs[i]; return NumCoeffs; } double *TrinomialMultiply( int FilterOrder, double *b, double *c ) { int i, j; double *RetVal; RetVal = (double *)calloc( 4 * FilterOrder, sizeof(double) ); if( RetVal == NULL ) return( NULL ); RetVal[2] = c[0]; RetVal[3] = c[1]; RetVal[0] = b[0]; RetVal[1] = b[1]; for( i = 1; i < FilterOrder; ++i ) { RetVal[2*(2*i+1)] += c[2*i] * RetVal[2*(2*i-1)] - c[2*i+1] * RetVal[2*(2*i-1)+1]; RetVal[2*(2*i+1)+1] += c[2*i] * RetVal[2*(2*i-1)+1] + c[2*i+1] * RetVal[2*(2*i-1)]; for( j = 2*i; j > 1; --j ) { RetVal[2*j] += b[2*i] * RetVal[2*(j-1)] - b[2*i+1] * RetVal[2*(j-1)+1] + c[2*i] * RetVal[2*(j-2)] - c[2*i+1] * RetVal[2*(j-2)+1]; RetVal[2*j+1] += b[2*i] * RetVal[2*(j-1)+1] + b[2*i+1] * RetVal[2*(j-1)] + c[2*i] * RetVal[2*(j-2)+1] + c[2*i+1] * RetVal[2*(j-2)]; } RetVal[2] += b[2*i] * RetVal[0] - b[2*i+1] * RetVal[1] + c[2*i]; RetVal[3] += b[2*i] * RetVal[1] + b[2*i+1] * RetVal[0] + c[2*i+1]; RetVal[0] += b[2*i]; RetVal[1] += b[2*i+1]; } return RetVal; } double *ComputeNumCoeffs(int FilterOrder) { double *TCoeffs; double *NumCoeffs; int i; NumCoeffs = (double *)calloc( 2*FilterOrder+1, sizeof(double) ); if( NumCoeffs == NULL ) return( NULL ); TCoeffs = ComputeHP(FilterOrder); if( TCoeffs == NULL ) return( NULL ); for( i = 0; i < FilterOrder; ++i) { NumCoeffs[2*i] = TCoeffs[i]; NumCoeffs[2*i+1] = 0.0; } NumCoeffs[2*FilterOrder] = TCoeffs[FilterOrder]; free(TCoeffs); return NumCoeffs; } double *ComputeDenCoeffs( int FilterOrder, double Lcutoff, double Ucutoff ) { int k; // loop variables double theta; // PI * (Ucutoff - Lcutoff) / 2.0 double cp; // cosine of phi double st; // sine of theta double ct; // cosine of theta double s2t; // sine of 2*theta double c2t; // cosine 0f 2*theta double *RCoeffs; // z^-2 coefficients double *TCoeffs; // z^-1 coefficients double *DenomCoeffs; // dk coefficients double PoleAngle; // pole angle double SinPoleAngle; // sine of pole angle double CosPoleAngle; // cosine of pole angle double a; // workspace variables cp = cos(PI * (Ucutoff + Lcutoff) / 2.0); theta = PI * (Ucutoff - Lcutoff) / 2.0; st = sin(theta); ct = cos(theta); s2t = 2.0*st*ct; // sine of 2*theta c2t = 2.0*ct*ct - 1.0; // cosine of 2*theta RCoeffs = (double *)calloc( 2 * FilterOrder, sizeof(double) ); TCoeffs = (double *)calloc( 2 * FilterOrder, sizeof(double) ); for( k = 0; k < FilterOrder; ++k ) { PoleAngle = PI * (double)(2*k+1)/(double)(2*FilterOrder); SinPoleAngle = sin(PoleAngle); CosPoleAngle = cos(PoleAngle); a = 1.0 + s2t*SinPoleAngle; RCoeffs[2*k] = c2t/a; RCoeffs[2*k+1] = s2t*CosPoleAngle/a; TCoeffs[2*k] = -2.0*cp*(ct+st*SinPoleAngle)/a; TCoeffs[2*k+1] = -2.0*cp*st*CosPoleAngle/a; } DenomCoeffs = TrinomialMultiply(FilterOrder, TCoeffs, RCoeffs ); free(TCoeffs); free(RCoeffs); DenomCoeffs[1] = DenomCoeffs[0]; DenomCoeffs[0] = 1.0; for( k = 3; k <= 2*FilterOrder; ++k ) DenomCoeffs[k] = DenomCoeffs[2*k-2]; return DenomCoeffs; } void filter(int ord, double *a, double *b, int np, double *x, double *y) { int i,j; y[0]=b[0] * x[0]; for (i=1;i<ord+1;i++) { y[i]=0.0; for (j=0;j<i+1;j++) y[i]=y[i]+b[j]*x[i-j]; for (j=0;j<i;j++) y[i]=y[i]-a[j+1]*y[i-j-1]; } for (i=ord+1;i<np+1;i++) { y[i]=0.0; for (j=0;j<ord+1;j++) y[i]=y[i]+b[j]*x[i-j]; for (j=0;j<ord;j++) y[i]=y[i]-a[j+1]*y[i-j-1]; } } int main(int argc, char *argv[]) { //Frequency bands is a vector of values - Lower Frequency Band and Higher Frequency Band //First value is lower cutoff and second value is higher cutoff double FrequencyBands[2] = {0.25,0.375};//these values are as a ratio of f/fs, where fs is sampling rate, and f is cutoff frequency //and therefore should lie in the range [0 1] //Filter Order int FiltOrd = 5; //Pixel Time Series /*int PixelTimeSeries[N]; int outputSeries[N]; */ //Create the variables for the numerator and denominator coefficients double *DenC = 0; double *NumC = 0; //Pass Numerator Coefficients and Denominator Coefficients arrays into function, will return the same NumC = ComputeNumCoeffs(FiltOrd); for(int k = 0; k<11; k++) { printf("NumC is: %lf\n", NumC[k]); } //is A in matlab function and the numbers are correct DenC = ComputeDenCoeffs(FiltOrd, FrequencyBands[0], FrequencyBands[1]); for(int k = 0; k<11; k++) { printf("DenC is: %lf\n", DenC[k]); } double y[5]; double x[5]={1,2,3,4,5}; filter(5, DenC, NumC, 5, x, y); return 1; }
I get this resutls for my code :
B= 1,0,-5,0,10,0,-10,0,5,0,-1 A= 1.000000000000000, -4.945988709743181, 13.556489496973796, -24.700711850327743, 32.994881546824828, -33.180726698160655, 25.546126213403539, -14.802008410165968, 6.285430089797051, -1.772929809750849, 0.277753012228403
but if I want to test the coefficinets in same frequency band in MATLAB, I get the following results:
>> [B, A]=butter(5, [0.25,0.375])
B = 0.0002, 0, -0.0008, 0, 0.0016, 0, -0.0016, 0, 0.0008, 0, -0.0002
A = 1.0000, -4.9460, 13.5565, -24.7007, 32.9948, -33.1806, 25.5461, -14.8020, 6.2854, -1.7729, 0.2778
I have test this website :http://www.exstrom.com/journal/sigproc/ code, but the result is equal as mine, not matlab. anybody knows why? or how can I get the same result as matlab toolbox?
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grantnz over 11 yearsDid you also have to modify the posted code for your filter function to get this to work properly? It looks like you may have some problems with the bounds. E.g. for (i=ord+1;i<np+1;i++) looks like it will step past the end of the x array.
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Admin over 11 yearsInteresting thread.. I transformed this into MATLAB and created my own Butterworth filter :) Thanks! By the way, your new edited "ComputeNumCoeffs" subroutine is only set up for
FilterOrder = 5
, since you are iteratingk=0-->11
. I know that it's easy to make it general.. but just wanted to alert whoever sees this thread later. -
BoltClock over 10 yearsYou need 50 reputation to post comments. Focus on answering questions and you should receive enough reputation to do so in no time.